LMFDB - Embedded newform 1925.2.a.r.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1925,2,Mod(1,1925)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1925, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1925 = 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1925.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.3712023891$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	1925.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -2.76393 q^{6} -1.00000 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -2.76393 q^{6} -1.00000 q^{7} -2.23607 q^{8} -1.47214 q^{9} -1.00000 q^{11} +3.70820 q^{12} -3.23607 q^{13} +2.23607 q^{14} -1.00000 q^{16} +3.23607 q^{17} +3.29180 q^{18} +6.47214 q^{19} -1.23607 q^{21} +2.23607 q^{22} -2.47214 q^{23} -2.76393 q^{24} +7.23607 q^{26} -5.52786 q^{27} -3.00000 q^{28} +8.47214 q^{29} -2.76393 q^{31} +6.70820 q^{32} -1.23607 q^{33} -7.23607 q^{34} -4.41641 q^{36} +8.47214 q^{37} -14.4721 q^{38} -4.00000 q^{39} -11.2361 q^{41} +2.76393 q^{42} -8.00000 q^{43} -3.00000 q^{44} +5.52786 q^{46} -2.76393 q^{47} -1.23607 q^{48} +1.00000 q^{49} +4.00000 q^{51} -9.70820 q^{52} +0.472136 q^{53} +12.3607 q^{54} +2.23607 q^{56} +8.00000 q^{57} -18.9443 q^{58} -1.23607 q^{59} -7.23607 q^{61} +6.18034 q^{62} +1.47214 q^{63} -13.0000 q^{64} +2.76393 q^{66} -14.4721 q^{67} +9.70820 q^{68} -3.05573 q^{69} -10.4721 q^{71} +3.29180 q^{72} +0.763932 q^{73} -18.9443 q^{74} +19.4164 q^{76} +1.00000 q^{77} +8.94427 q^{78} -8.94427 q^{79} -2.41641 q^{81} +25.1246 q^{82} +11.4164 q^{83} -3.70820 q^{84} +17.8885 q^{86} +10.4721 q^{87} +2.23607 q^{88} +2.00000 q^{89} +3.23607 q^{91} -7.41641 q^{92} -3.41641 q^{93} +6.18034 q^{94} +8.29180 q^{96} -17.4164 q^{97} -2.23607 q^{98} +1.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 6 q^{4} - 10 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + 6 * q^4 - 10 * q^6 - 2 * q^7 + 6 * q^9	$ 2 q - 2 q^{3} + 6 q^{4} - 10 q^{6} - 2 q^{7} + 6 q^{9} - 2 q^{11} - 6 q^{12} - 2 q^{13} - 2 q^{16} + 2 q^{17} + 20 q^{18} + 4 q^{19} + 2 q^{21} + 4 q^{23} - 10 q^{24} + 10 q^{26} - 20 q^{27} - 6 q^{28} + 8 q^{29} - 10 q^{31} + 2 q^{33} - 10 q^{34} + 18 q^{36} + 8 q^{37} - 20 q^{38} - 8 q^{39} - 18 q^{41} + 10 q^{42} - 16 q^{43} - 6 q^{44} + 20 q^{46} - 10 q^{47} + 2 q^{48} + 2 q^{49} + 8 q^{51} - 6 q^{52} - 8 q^{53} - 20 q^{54} + 16 q^{57} - 20 q^{58} + 2 q^{59} - 10 q^{61} - 10 q^{62} - 6 q^{63} - 26 q^{64} + 10 q^{66} - 20 q^{67} + 6 q^{68} - 24 q^{69} - 12 q^{71} + 20 q^{72} + 6 q^{73} - 20 q^{74} + 12 q^{76} + 2 q^{77} + 22 q^{81} + 10 q^{82} - 4 q^{83} + 6 q^{84} + 12 q^{87} + 4 q^{89} + 2 q^{91} + 12 q^{92} + 20 q^{93} - 10 q^{94} + 30 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 6 * q^4 - 10 * q^6 - 2 * q^7 + 6 * q^9 - 2 * q^11 - 6 * q^12 - 2 * q^13 - 2 * q^16 + 2 * q^17 + 20 * q^18 + 4 * q^19 + 2 * q^21 + 4 * q^23 - 10 * q^24 + 10 * q^26 - 20 * q^27 - 6 * q^28 + 8 * q^29 - 10 * q^31 + 2 * q^33 - 10 * q^34 + 18 * q^36 + 8 * q^37 - 20 * q^38 - 8 * q^39 - 18 * q^41 + 10 * q^42 - 16 * q^43 - 6 * q^44 + 20 * q^46 - 10 * q^47 + 2 * q^48 + 2 * q^49 + 8 * q^51 - 6 * q^52 - 8 * q^53 - 20 * q^54 + 16 * q^57 - 20 * q^58 + 2 * q^59 - 10 * q^61 - 10 * q^62 - 6 * q^63 - 26 * q^64 + 10 * q^66 - 20 * q^67 + 6 * q^68 - 24 * q^69 - 12 * q^71 + 20 * q^72 + 6 * q^73 - 20 * q^74 + 12 * q^76 + 2 * q^77 + 22 * q^81 + 10 * q^82 - 4 * q^83 + 6 * q^84 + 12 * q^87 + 4 * q^89 + 2 * q^91 + 12 * q^92 + 20 * q^93 - 10 * q^94 + 30 * q^96 - 8 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	1.23607	0.713644	0.356822	−	0.934172i	$-0.383860\pi$
$3$	1.23607	0.713644	0.356822	+	0.934172i	$0.383860\pi$
$4$	3.00000	1.50000
$5$	0	0
$5$	0	0
$6$	−2.76393	−1.12837
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.23607	−0.790569
$9$	−1.47214	−0.490712
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.70820	1.07047
$13$	−3.23607	−0.897524	−0.448762	−	0.893651i	$-0.648135\pi$
$13$	−3.23607	−0.897524	−0.448762	+	0.893651i	$0.648135\pi$
$14$	2.23607	0.597614
$15$	0	0
$16$	−1.00000	−0.250000
$17$	3.23607	0.784862	0.392431	−	0.919781i	$-0.371634\pi$
$17$	3.23607	0.784862	0.392431	+	0.919781i	$0.371634\pi$
$18$	3.29180	0.775884
$19$	6.47214	1.48481	0.742405	−	0.669951i	$-0.233685\pi$
$19$	6.47214	1.48481	0.742405	+	0.669951i	$0.233685\pi$
$20$	0	0
$21$	−1.23607	−0.269732
$22$	2.23607	0.476731
$23$	−2.47214	−0.515476	−0.257738	−	0.966215i	$-0.582977\pi$
$23$	−2.47214	−0.515476	−0.257738	+	0.966215i	$0.582977\pi$
$24$	−2.76393	−0.564185
$25$	0	0
$26$	7.23607	1.41911
$27$	−5.52786	−1.06384
$28$	−3.00000	−0.566947
$29$	8.47214	1.57324	0.786618	−	0.617440i	$-0.211830\pi$
$29$	8.47214	1.57324	0.786618	+	0.617440i	$0.211830\pi$
$30$	0	0
$31$	−2.76393	−0.496417	−0.248208	−	0.968707i	$-0.579842\pi$
$31$	−2.76393	−0.496417	−0.248208	+	0.968707i	$0.579842\pi$
$32$	6.70820	1.18585
$33$	−1.23607	−0.215172
$34$	−7.23607	−1.24098
$35$	0	0
$36$	−4.41641	−0.736068
$37$	8.47214	1.39281	0.696405	−	0.717649i	$-0.254782\pi$
$37$	8.47214	1.39281	0.696405	+	0.717649i	$0.254782\pi$
$38$	−14.4721	−2.34769
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−11.2361	−1.75478	−0.877390	−	0.479779i	$-0.840717\pi$
$41$	−11.2361	−1.75478	−0.877390	+	0.479779i	$0.840717\pi$
$42$	2.76393	0.426484
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−3.00000	−0.452267
$45$	0	0
$46$	5.52786	0.815039
$47$	−2.76393	−0.403161	−0.201580	−	0.979472i	$-0.564608\pi$
$47$	−2.76393	−0.403161	−0.201580	+	0.979472i	$0.564608\pi$
$48$	−1.23607	−0.178411
$49$	1.00000	0.142857
$50$	0	0
$51$	4.00000	0.560112
$52$	−9.70820	−1.34629
$53$	0.472136	0.0648529	0.0324264	−	0.999474i	$-0.489677\pi$
$53$	0.472136	0.0648529	0.0324264	+	0.999474i	$0.489677\pi$
$54$	12.3607	1.68208
$55$	0	0
$56$	2.23607	0.298807
$57$	8.00000	1.05963
$58$	−18.9443	−2.48750
$59$	−1.23607	−0.160922	−0.0804612	−	0.996758i	$-0.525639\pi$
$59$	−1.23607	−0.160922	−0.0804612	+	0.996758i	$0.525639\pi$
$60$	0	0
$61$	−7.23607	−0.926484	−0.463242	−	0.886232i	$-0.653314\pi$
$61$	−7.23607	−0.926484	−0.463242	+	0.886232i	$0.653314\pi$
$62$	6.18034	0.784904
$63$	1.47214	0.185472
$64$	−13.0000	−1.62500
$65$	0	0
$66$	2.76393	0.340217
$67$	−14.4721	−1.76805	−0.884026	−	0.467437i	$-0.845177\pi$
$67$	−14.4721	−1.76805	−0.884026	+	0.467437i	$0.845177\pi$
$68$	9.70820	1.17729
$69$	−3.05573	−0.367866
$70$	0	0
$71$	−10.4721	−1.24281	−0.621407	−	0.783488i	$-0.713439\pi$
$71$	−10.4721	−1.24281	−0.621407	+	0.783488i	$0.713439\pi$
$72$	3.29180	0.387942
$73$	0.763932	0.0894115	0.0447057	−	0.999000i	$-0.485765\pi$
$73$	0.763932	0.0894115	0.0447057	+	0.999000i	$0.485765\pi$
$74$	−18.9443	−2.20223
$75$	0	0
$76$	19.4164	2.22721
$77$	1.00000	0.113961
$78$	8.94427	1.01274
$79$	−8.94427	−1.00631	−0.503155	−	0.864196i	$-0.667827\pi$
$79$	−8.94427	−1.00631	−0.503155	+	0.864196i	$0.667827\pi$
$80$	0	0
$81$	−2.41641	−0.268490
$82$	25.1246	2.77455
$83$	11.4164	1.25311	0.626557	−	0.779376i	$-0.284464\pi$
$83$	11.4164	1.25311	0.626557	+	0.779376i	$0.284464\pi$
$84$	−3.70820	−0.404598
$85$	0	0
$86$	17.8885	1.92897
$87$	10.4721	1.12273
$88$	2.23607	0.238366
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	3.23607	0.339232
$92$	−7.41641	−0.773214
$93$	−3.41641	−0.354265
$94$	6.18034	0.637453
$95$	0	0
$96$	8.29180	0.846278
$97$	−17.4164	−1.76837	−0.884184	−	0.467139i	$-0.845285\pi$
$97$	−17.4164	−1.76837	−0.884184	+	0.467139i	$0.845285\pi$
$98$	−2.23607	−0.225877
$99$	1.47214	0.147955
$100$	0	0
$101$	−4.76393	−0.474029	−0.237014	−	0.971506i	$-0.576169\pi$
$101$	−4.76393	−0.474029	−0.237014	+	0.971506i	$0.576169\pi$
$102$	−8.94427	−0.885615
$103$	−7.70820	−0.759512	−0.379756	−	0.925087i	$-0.623992\pi$
$103$	−7.70820	−0.759512	−0.379756	+	0.925087i	$0.623992\pi$
$104$	7.23607	0.709555
$105$	0	0
$106$	−1.05573	−0.102541
$107$	4.00000	0.386695	0.193347	−	0.981130i	$-0.438066\pi$
$107$	4.00000	0.386695	0.193347	+	0.981130i	$0.438066\pi$
$108$	−16.5836	−1.59576
$109$	−4.47214	−0.428353	−0.214176	−	0.976795i	$-0.568707\pi$
$109$	−4.47214	−0.428353	−0.214176	+	0.976795i	$0.568707\pi$
$110$	0	0
$111$	10.4721	0.993971
$112$	1.00000	0.0944911
$113$	−2.00000	−0.188144	−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000	−0.188144	−0.0940721	+	0.995565i	$0.529988\pi$
$114$	−17.8885	−1.67542
$115$	0	0
$116$	25.4164	2.35985
$117$	4.76393	0.440426
$118$	2.76393	0.254441
$119$	−3.23607	−0.296650
$120$	0	0
$121$	1.00000	0.0909091
$122$	16.1803	1.46490
$123$	−13.8885	−1.25229
$124$	−8.29180	−0.744625
$125$	0	0
$126$	−3.29180	−0.293257
$127$	−3.05573	−0.271152	−0.135576	−	0.990767i	$-0.543288\pi$
$127$	−3.05573	−0.271152	−0.135576	+	0.990767i	$0.543288\pi$
$128$	15.6525	1.38350
$129$	−9.88854	−0.870638
$130$	0	0
$131$	21.8885	1.91241	0.956205	−	0.292696i	$-0.0945525\pi$
$131$	21.8885	1.91241	0.956205	+	0.292696i	$0.0945525\pi$
$132$	−3.70820	−0.322758
$133$	−6.47214	−0.561205
$134$	32.3607	2.79554
$135$	0	0
$136$	−7.23607	−0.620488
$137$	−16.4721	−1.40731	−0.703655	−	0.710542i	$-0.748450\pi$
$137$	−16.4721	−1.40731	−0.703655	+	0.710542i	$0.748450\pi$
$138$	6.83282	0.581648
$139$	−1.52786	−0.129592	−0.0647959	−	0.997899i	$-0.520640\pi$
$139$	−1.52786	−0.129592	−0.0647959	+	0.997899i	$0.520640\pi$
$140$	0	0
$141$	−3.41641	−0.287713
$142$	23.4164	1.96506
$143$	3.23607	0.270614
$144$	1.47214	0.122678
$145$	0	0
$146$	−1.70820	−0.141372
$147$	1.23607	0.101949
$148$	25.4164	2.08922
$149$	14.0000	1.14692	0.573462	−	0.819232i	$-0.305600\pi$
$149$	14.0000	1.14692	0.573462	+	0.819232i	$0.305600\pi$
$150$	0	0
$151$	8.94427	0.727875	0.363937	−	0.931423i	$-0.381432\pi$
$151$	8.94427	0.727875	0.363937	+	0.931423i	$0.381432\pi$
$152$	−14.4721	−1.17385
$153$	−4.76393	−0.385141
$154$	−2.23607	−0.180187
$155$	0	0
$156$	−12.0000	−0.960769
$157$	−10.9443	−0.873448	−0.436724	−	0.899596i	$-0.643861\pi$
$157$	−10.9443	−0.873448	−0.436724	+	0.899596i	$0.643861\pi$
$158$	20.0000	1.59111
$159$	0.583592	0.0462819
$160$	0	0
$161$	2.47214	0.194832
$162$	5.40325	0.424520
$163$	3.41641	0.267594	0.133797	−	0.991009i	$-0.457283\pi$
$163$	3.41641	0.267594	0.133797	+	0.991009i	$0.457283\pi$
$164$	−33.7082	−2.63217
$165$	0	0
$166$	−25.5279	−1.98135
$167$	−4.94427	−0.382599	−0.191300	−	0.981532i	$-0.561270\pi$
$167$	−4.94427	−0.382599	−0.191300	+	0.981532i	$0.561270\pi$
$168$	2.76393	0.213242
$169$	−2.52786	−0.194451
$170$	0	0
$171$	−9.52786	−0.728614
$172$	−24.0000	−1.82998
$173$	12.7639	0.970424	0.485212	−	0.874397i	$-0.338742\pi$
$173$	12.7639	0.970424	0.485212	+	0.874397i	$0.338742\pi$
$174$	−23.4164	−1.77519
$175$	0	0
$176$	1.00000	0.0753778
$177$	−1.52786	−0.114841
$178$	−4.47214	−0.335201
$179$	−8.94427	−0.668526	−0.334263	−	0.942480i	$-0.608487\pi$
$179$	−8.94427	−0.668526	−0.334263	+	0.942480i	$0.608487\pi$
$180$	0	0
$181$	−25.4164	−1.88919	−0.944593	−	0.328243i	$-0.893544\pi$
$181$	−25.4164	−1.88919	−0.944593	+	0.328243i	$0.893544\pi$
$182$	−7.23607	−0.536373
$183$	−8.94427	−0.661180
$184$	5.52786	0.407520
$185$	0	0
$186$	7.63932	0.560142
$187$	−3.23607	−0.236645
$188$	−8.29180	−0.604741
$189$	5.52786	0.402093
$190$	0	0
$191$	−3.05573	−0.221105	−0.110552	−	0.993870i	$-0.535262\pi$
$191$	−3.05573	−0.221105	−0.110552	+	0.993870i	$0.535262\pi$
$192$	−16.0689	−1.15967
$193$	−11.8885	−0.855756	−0.427878	−	0.903836i	$-0.640739\pi$
$193$	−11.8885	−0.855756	−0.427878	+	0.903836i	$0.640739\pi$
$194$	38.9443	2.79604
$195$	0	0
$196$	3.00000	0.214286
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	−3.29180	−0.233938
$199$	−2.18034	−0.154560	−0.0772801	−	0.997009i	$-0.524624\pi$
$199$	−2.18034	−0.154560	−0.0772801	+	0.997009i	$0.524624\pi$
$200$	0	0
$201$	−17.8885	−1.26176
$202$	10.6525	0.749506
$203$	−8.47214	−0.594627
$204$	12.0000	0.840168
$205$	0	0
$206$	17.2361	1.20089
$207$	3.63932	0.252950
$208$	3.23607	0.224381
$209$	−6.47214	−0.447687
$210$	0	0
$211$	−13.8885	−0.956127	−0.478063	−	0.878325i	$-0.658661\pi$
$211$	−13.8885	−0.956127	−0.478063	+	0.878325i	$0.658661\pi$
$212$	1.41641	0.0972793
$213$	−12.9443	−0.886927
$214$	−8.94427	−0.611418
$215$	0	0
$216$	12.3607	0.841038
$217$	2.76393	0.187628
$218$	10.0000	0.677285
$219$	0.944272	0.0638080
$220$	0	0
$221$	−10.4721	−0.704432
$222$	−23.4164	−1.57161
$223$	10.1803	0.681726	0.340863	−	0.940113i	$-0.389281\pi$
$223$	10.1803	0.681726	0.340863	+	0.940113i	$0.389281\pi$
$224$	−6.70820	−0.448211
$225$	0	0
$226$	4.47214	0.297482
$227$	−5.88854	−0.390836	−0.195418	−	0.980720i	$-0.562606\pi$
$227$	−5.88854	−0.390836	−0.195418	+	0.980720i	$0.562606\pi$
$228$	24.0000	1.58944
$229$	−4.47214	−0.295527	−0.147764	−	0.989023i	$-0.547207\pi$
$229$	−4.47214	−0.295527	−0.147764	+	0.989023i	$0.547207\pi$
$230$	0	0
$231$	1.23607	0.0813273
$232$	−18.9443	−1.24375
$233$	−9.41641	−0.616889	−0.308445	−	0.951242i	$-0.599808\pi$
$233$	−9.41641	−0.616889	−0.308445	+	0.951242i	$0.599808\pi$
$234$	−10.6525	−0.696374
$235$	0	0
$236$	−3.70820	−0.241384
$237$	−11.0557	−0.718147
$238$	7.23607	0.469045
$239$	−9.88854	−0.639637	−0.319818	−	0.947479i	$-0.603622\pi$
$239$	−9.88854	−0.639637	−0.319818	+	0.947479i	$0.603622\pi$
$240$	0	0
$241$	−13.1246	−0.845431	−0.422715	−	0.906263i	$-0.638923\pi$
$241$	−13.1246	−0.845431	−0.422715	+	0.906263i	$0.638923\pi$
$242$	−2.23607	−0.143740
$243$	13.5967	0.872232
$244$	−21.7082	−1.38973
$245$	0	0
$246$	31.0557	1.98004
$247$	−20.9443	−1.33265
$248$	6.18034	0.392452
$249$	14.1115	0.894277
$250$	0	0
$251$	4.29180	0.270896	0.135448	−	0.990784i	$-0.456753\pi$
$251$	4.29180	0.270896	0.135448	+	0.990784i	$0.456753\pi$
$252$	4.41641	0.278208
$253$	2.47214	0.155422
$254$	6.83282	0.428729
$255$	0	0
$256$	−9.00000	−0.562500
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	22.1115	1.37660
$259$	−8.47214	−0.526433
$260$	0	0
$261$	−12.4721	−0.772006
$262$	−48.9443	−3.02379
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	2.76393	0.170108
$265$	0	0
$266$	14.4721	0.887344
$267$	2.47214	0.151292
$268$	−43.4164	−2.65208
$269$	13.4164	0.818013	0.409006	−	0.912532i	$-0.365875\pi$
$269$	13.4164	0.818013	0.409006	+	0.912532i	$0.365875\pi$
$270$	0	0
$271$	−10.4721	−0.636137	−0.318068	−	0.948068i	$-0.603034\pi$
$271$	−10.4721	−0.636137	−0.318068	+	0.948068i	$0.603034\pi$
$272$	−3.23607	−0.196215
$273$	4.00000	0.242091
$274$	36.8328	2.22515
$275$	0	0
$276$	−9.16718	−0.551800
$277$	19.8885	1.19499	0.597493	−	0.801874i	$-0.296163\pi$
$277$	19.8885	1.19499	0.597493	+	0.801874i	$0.296163\pi$
$278$	3.41641	0.204903
$279$	4.06888	0.243598
$280$	0	0
$281$	−3.52786	−0.210455	−0.105227	−	0.994448i	$-0.533557\pi$
$281$	−3.52786	−0.210455	−0.105227	+	0.994448i	$0.533557\pi$
$282$	7.63932	0.454915
$283$	−29.8885	−1.77669	−0.888345	−	0.459177i	$-0.848144\pi$
$283$	−29.8885	−1.77669	−0.888345	+	0.459177i	$0.848144\pi$
$284$	−31.4164	−1.86422
$285$	0	0
$286$	−7.23607	−0.427878
$287$	11.2361	0.663244
$288$	−9.87539	−0.581913
$289$	−6.52786	−0.383992
$290$	0	0
$291$	−21.5279	−1.26199
$292$	2.29180	0.134117
$293$	25.1246	1.46780	0.733898	−	0.679260i	$-0.237699\pi$
$293$	25.1246	1.46780	0.733898	+	0.679260i	$0.237699\pi$
$294$	−2.76393	−0.161196
$295$	0	0
$296$	−18.9443	−1.10111
$297$	5.52786	0.320759
$298$	−31.3050	−1.81345
$299$	8.00000	0.462652
$300$	0	0
$301$	8.00000	0.461112
$302$	−20.0000	−1.15087
$303$	−5.88854	−0.338288
$304$	−6.47214	−0.371202
$305$	0	0
$306$	10.6525	0.608962
$307$	8.94427	0.510477	0.255238	−	0.966878i	$-0.417846\pi$
$307$	8.94427	0.510477	0.255238	+	0.966878i	$0.417846\pi$
$308$	3.00000	0.170941
$309$	−9.52786	−0.542021
$310$	0	0
$311$	−8.29180	−0.470185	−0.235092	−	0.971973i	$-0.575539\pi$
$311$	−8.29180	−0.470185	−0.235092	+	0.971973i	$0.575539\pi$
$312$	8.94427	0.506370
$313$	−14.9443	−0.844700	−0.422350	−	0.906433i	$-0.638795\pi$
$313$	−14.9443	−0.844700	−0.422350	+	0.906433i	$0.638795\pi$
$314$	24.4721	1.38104
$315$	0	0
$316$	−26.8328	−1.50946
$317$	−14.0000	−0.786318	−0.393159	−	0.919470i	$-0.628618\pi$
$317$	−14.0000	−0.786318	−0.393159	+	0.919470i	$0.628618\pi$
$318$	−1.30495	−0.0731781
$319$	−8.47214	−0.474349
$320$	0	0
$321$	4.94427	0.275962
$322$	−5.52786	−0.308056
$323$	20.9443	1.16537
$324$	−7.24922	−0.402735
$325$	0	0
$326$	−7.63932	−0.423103
$327$	−5.52786	−0.305692
$328$	25.1246	1.38727
$329$	2.76393	0.152381
$330$	0	0
$331$	−13.8885	−0.763383	−0.381692	−	0.924290i	$-0.624658\pi$
$331$	−13.8885	−0.763383	−0.381692	+	0.924290i	$0.624658\pi$
$332$	34.2492	1.87967
$333$	−12.4721	−0.683469
$334$	11.0557	0.604943
$335$	0	0
$336$	1.23607	0.0674330
$337$	11.5279	0.627963	0.313981	−	0.949429i	$-0.398337\pi$
$337$	11.5279	0.627963	0.313981	+	0.949429i	$0.398337\pi$
$338$	5.65248	0.307454
$339$	−2.47214	−0.134268
$340$	0	0
$341$	2.76393	0.149675
$342$	21.3050	1.15204
$343$	−1.00000	−0.0539949
$344$	17.8885	0.964486
$345$	0	0
$346$	−28.5410	−1.53437
$347$	−20.9443	−1.12435	−0.562174	−	0.827019i	$-0.690035\pi$
$347$	−20.9443	−1.12435	−0.562174	+	0.827019i	$0.690035\pi$
$348$	31.4164	1.68410
$349$	−7.23607	−0.387338	−0.193669	−	0.981067i	$-0.562039\pi$
$349$	−7.23607	−0.387338	−0.193669	+	0.981067i	$0.562039\pi$
$350$	0	0
$351$	17.8885	0.954820
$352$	−6.70820	−0.357548
$353$	−19.8885	−1.05856	−0.529280	−	0.848447i	$-0.677538\pi$
$353$	−19.8885	−1.05856	−0.529280	+	0.848447i	$0.677538\pi$
$354$	3.41641	0.181580
$355$	0	0
$356$	6.00000	0.317999
$357$	−4.00000	−0.211702
$358$	20.0000	1.05703
$359$	−24.9443	−1.31651	−0.658254	−	0.752796i	$-0.728705\pi$
$359$	−24.9443	−1.31651	−0.658254	+	0.752796i	$0.728705\pi$
$360$	0	0
$361$	22.8885	1.20466
$362$	56.8328	2.98707
$363$	1.23607	0.0648767
$364$	9.70820	0.508848
$365$	0	0
$366$	20.0000	1.04542
$367$	23.1246	1.20709	0.603547	−	0.797327i	$-0.293753\pi$
$367$	23.1246	1.20709	0.603547	+	0.797327i	$0.293753\pi$
$368$	2.47214	0.128869
$369$	16.5410	0.861091
$370$	0	0
$371$	−0.472136	−0.0245121
$372$	−10.2492	−0.531397
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	7.23607	0.374168
$375$	0	0
$376$	6.18034	0.318727
$377$	−27.4164	−1.41202
$378$	−12.3607	−0.635765
$379$	37.3050	1.91623	0.958113	−	0.286389i	$-0.0924551\pi$
$379$	37.3050	1.91623	0.958113	+	0.286389i	$0.0924551\pi$
$380$	0	0
$381$	−3.77709	−0.193506
$382$	6.83282	0.349597
$383$	4.65248	0.237730	0.118865	−	0.992910i	$-0.462074\pi$
$383$	4.65248	0.237730	0.118865	+	0.992910i	$0.462074\pi$
$384$	19.3475	0.987324
$385$	0	0
$386$	26.5836	1.35307
$387$	11.7771	0.598663
$388$	−52.2492	−2.65255
$389$	15.8885	0.805581	0.402791	−	0.915292i	$-0.368040\pi$
$389$	15.8885	0.805581	0.402791	+	0.915292i	$0.368040\pi$
$390$	0	0
$391$	−8.00000	−0.404577
$392$	−2.23607	−0.112938
$393$	27.0557	1.36478
$394$	−4.47214	−0.225303
$395$	0	0
$396$	4.41641	0.221933
$397$	35.8885	1.80119	0.900597	−	0.434655i	$-0.143130\pi$
$397$	35.8885	1.80119	0.900597	+	0.434655i	$0.143130\pi$
$398$	4.87539	0.244381
$399$	−8.00000	−0.400501
$400$	0	0
$401$	22.9443	1.14578	0.572891	−	0.819631i	$-0.305822\pi$
$401$	22.9443	1.14578	0.572891	+	0.819631i	$0.305822\pi$
$402$	40.0000	1.99502
$403$	8.94427	0.445546
$404$	−14.2918	−0.711043
$405$	0	0
$406$	18.9443	0.940188
$407$	−8.47214	−0.419948
$408$	−8.94427	−0.442807
$409$	9.12461	0.451183	0.225592	−	0.974222i	$-0.427569\pi$
$409$	9.12461	0.451183	0.225592	+	0.974222i	$0.427569\pi$
$410$	0	0
$411$	−20.3607	−1.00432
$412$	−23.1246	−1.13927
$413$	1.23607	0.0608229
$414$	−8.13777	−0.399949
$415$	0	0
$416$	−21.7082	−1.06433
$417$	−1.88854	−0.0924824
$418$	14.4721	0.707855
$419$	24.6525	1.20435	0.602176	−	0.798363i	$-0.294300\pi$
$419$	24.6525	1.20435	0.602176	+	0.798363i	$0.294300\pi$
$420$	0	0
$421$	22.3607	1.08979	0.544896	−	0.838503i	$-0.316569\pi$
$421$	22.3607	1.08979	0.544896	+	0.838503i	$0.316569\pi$
$422$	31.0557	1.51177
$423$	4.06888	0.197836
$424$	−1.05573	−0.0512707
$425$	0	0
$426$	28.9443	1.40235
$427$	7.23607	0.350178
$428$	12.0000	0.580042
$429$	4.00000	0.193122
$430$	0	0
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	5.52786	0.265959
$433$	8.47214	0.407145	0.203572	−	0.979060i	$-0.434745\pi$
$433$	8.47214	0.407145	0.203572	+	0.979060i	$0.434745\pi$
$434$	−6.18034	−0.296666
$435$	0	0
$436$	−13.4164	−0.642529
$437$	−16.0000	−0.765384
$438$	−2.11146	−0.100889
$439$	10.4721	0.499808	0.249904	−	0.968271i	$-0.419601\pi$
$439$	10.4721	0.499808	0.249904	+	0.968271i	$0.419601\pi$
$440$	0	0
$441$	−1.47214	−0.0701017
$442$	23.4164	1.11380
$443$	24.9443	1.18514	0.592569	−	0.805520i	$-0.298114\pi$
$443$	24.9443	1.18514	0.592569	+	0.805520i	$0.298114\pi$
$444$	31.4164	1.49096
$445$	0	0
$446$	−22.7639	−1.07790
$447$	17.3050	0.818496
$448$	13.0000	0.614192
$449$	−28.4721	−1.34368	−0.671842	−	0.740695i	$-0.734496\pi$
$449$	−28.4721	−1.34368	−0.671842	+	0.740695i	$0.734496\pi$
$450$	0	0
$451$	11.2361	0.529086
$452$	−6.00000	−0.282216
$453$	11.0557	0.519443
$454$	13.1672	0.617967
$455$	0	0
$456$	−17.8885	−0.837708
$457$	28.8328	1.34874	0.674371	−	0.738393i	$-0.264415\pi$
$457$	28.8328	1.34874	0.674371	+	0.738393i	$0.264415\pi$
$458$	10.0000	0.467269
$459$	−17.8885	−0.834966
$460$	0	0
$461$	−12.1803	−0.567295	−0.283647	−	0.958929i	$-0.591545\pi$
$461$	−12.1803	−0.567295	−0.283647	+	0.958929i	$0.591545\pi$
$462$	−2.76393	−0.128590
$463$	5.52786	0.256902	0.128451	−	0.991716i	$-0.459000\pi$
$463$	5.52786	0.256902	0.128451	+	0.991716i	$0.459000\pi$
$464$	−8.47214	−0.393309
$465$	0	0
$466$	21.0557	0.975388
$467$	−24.0689	−1.11378	−0.556888	−	0.830588i	$-0.688005\pi$
$467$	−24.0689	−1.11378	−0.556888	+	0.830588i	$0.688005\pi$
$468$	14.2918	0.660639
$469$	14.4721	0.668261
$470$	0	0
$471$	−13.5279	−0.623331
$472$	2.76393	0.127220
$473$	8.00000	0.367840
$474$	24.7214	1.13549
$475$	0	0
$476$	−9.70820	−0.444975
$477$	−0.695048	−0.0318241
$478$	22.1115	1.01135
$479$	13.5279	0.618104	0.309052	−	0.951045i	$-0.399988\pi$
$479$	13.5279	0.618104	0.309052	+	0.951045i	$0.399988\pi$
$480$	0	0
$481$	−27.4164	−1.25008
$482$	29.3475	1.33674
$483$	3.05573	0.139040
$484$	3.00000	0.136364
$485$	0	0
$486$	−30.4033	−1.37912
$487$	36.3607	1.64766	0.823830	−	0.566837i	$-0.191833\pi$
$487$	36.3607	1.64766	0.823830	+	0.566837i	$0.191833\pi$
$488$	16.1803	0.732450
$489$	4.22291	0.190967
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	−41.6656	−1.87843
$493$	27.4164	1.23477
$494$	46.8328	2.10711
$495$	0	0
$496$	2.76393	0.124104
$497$	10.4721	0.469739
$498$	−31.5542	−1.41398
$499$	1.52786	0.0683966	0.0341983	−	0.999415i	$-0.489112\pi$
$499$	1.52786	0.0683966	0.0341983	+	0.999415i	$0.489112\pi$
$500$	0	0
$501$	−6.11146	−0.273040
$502$	−9.59675	−0.428324
$503$	−23.4164	−1.04409	−0.522043	−	0.852919i	$-0.674830\pi$
$503$	−23.4164	−1.04409	−0.522043	+	0.852919i	$0.674830\pi$
$504$	−3.29180	−0.146628
$505$	0	0
$506$	−5.52786	−0.245744
$507$	−3.12461	−0.138769
$508$	−9.16718	−0.406728
$509$	40.4721	1.79390	0.896948	−	0.442136i	$-0.145779\pi$
$509$	40.4721	1.79390	0.896948	+	0.442136i	$0.145779\pi$
$510$	0	0
$511$	−0.763932	−0.0337944
$512$	−11.1803	−0.494106
$513$	−35.7771	−1.57960
$514$	−13.4164	−0.591772
$515$	0	0
$516$	−29.6656	−1.30596
$517$	2.76393	0.121558
$518$	18.9443	0.832364
$519$	15.7771	0.692537
$520$	0	0
$521$	30.3607	1.33013	0.665063	−	0.746787i	$-0.268405\pi$
$521$	30.3607	1.33013	0.665063	+	0.746787i	$0.268405\pi$
$522$	27.8885	1.22065
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	65.6656	2.86862
$525$	0	0
$526$	0	0
$527$	−8.94427	−0.389619
$528$	1.23607	0.0537930
$529$	−16.8885	−0.734285
$530$	0	0
$531$	1.81966	0.0789665
$532$	−19.4164	−0.841808
$533$	36.3607	1.57496
$534$	−5.52786	−0.239214
$535$	0	0
$536$	32.3607	1.39777
$537$	−11.0557	−0.477090
$538$	−30.0000	−1.29339
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	20.8328	0.895673	0.447836	−	0.894116i	$-0.352195\pi$
$541$	20.8328	0.895673	0.447836	+	0.894116i	$0.352195\pi$
$542$	23.4164	1.00582
$543$	−31.4164	−1.34821
$544$	21.7082	0.930732
$545$	0	0
$546$	−8.94427	−0.382780
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−49.4164	−2.11096
$549$	10.6525	0.454637
$550$	0	0
$551$	54.8328	2.33596
$552$	6.83282	0.290824
$553$	8.94427	0.380349
$554$	−44.4721	−1.88944
$555$	0	0
$556$	−4.58359	−0.194388
$557$	38.9443	1.65012	0.825061	−	0.565044i	$-0.191141\pi$
$557$	38.9443	1.65012	0.825061	+	0.565044i	$0.191141\pi$
$558$	−9.09830	−0.385162
$559$	25.8885	1.09497
$560$	0	0
$561$	−4.00000	−0.168880
$562$	7.88854	0.332758
$563$	−12.5836	−0.530335	−0.265168	−	0.964202i	$-0.585427\pi$
$563$	−12.5836	−0.530335	−0.265168	+	0.964202i	$0.585427\pi$
$564$	−10.2492	−0.431570
$565$	0	0
$566$	66.8328	2.80919
$567$	2.41641	0.101480
$568$	23.4164	0.982531
$569$	7.52786	0.315584	0.157792	−	0.987472i	$-0.449562\pi$
$569$	7.52786	0.315584	0.157792	+	0.987472i	$0.449562\pi$
$570$	0	0
$571$	−15.0557	−0.630063	−0.315031	−	0.949081i	$-0.602015\pi$
$571$	−15.0557	−0.630063	−0.315031	+	0.949081i	$0.602015\pi$
$572$	9.70820	0.405920
$573$	−3.77709	−0.157790
$574$	−25.1246	−1.04868
$575$	0	0
$576$	19.1378	0.797407
$577$	19.5279	0.812956	0.406478	−	0.913661i	$-0.366757\pi$
$577$	19.5279	0.812956	0.406478	+	0.913661i	$0.366757\pi$
$578$	14.5967	0.607145
$579$	−14.6950	−0.610705
$580$	0	0
$581$	−11.4164	−0.473632
$582$	48.1378	1.99537
$583$	−0.472136	−0.0195539
$584$	−1.70820	−0.0706860
$585$	0	0
$586$	−56.1803	−2.32079
$587$	−27.1246	−1.11955	−0.559776	−	0.828644i	$-0.689113\pi$
$587$	−27.1246	−1.11955	−0.559776	+	0.828644i	$0.689113\pi$
$588$	3.70820	0.152924
$589$	−17.8885	−0.737085
$590$	0	0
$591$	2.47214	0.101690
$592$	−8.47214	−0.348203
$593$	45.7082	1.87701	0.938505	−	0.345264i	$-0.112211\pi$
$593$	45.7082	1.87701	0.938505	+	0.345264i	$0.112211\pi$
$594$	−12.3607	−0.507165
$595$	0	0
$596$	42.0000	1.72039
$597$	−2.69505	−0.110301
$598$	−17.8885	−0.731517
$599$	−23.4164	−0.956768	−0.478384	−	0.878151i	$-0.658777\pi$
$599$	−23.4164	−0.956768	−0.478384	+	0.878151i	$0.658777\pi$
$600$	0	0
$601$	−37.1246	−1.51434	−0.757172	−	0.653215i	$-0.773420\pi$
$601$	−37.1246	−1.51434	−0.757172	+	0.653215i	$0.773420\pi$
$602$	−17.8885	−0.729083
$603$	21.3050	0.867605
$604$	26.8328	1.09181
$605$	0	0
$606$	13.1672	0.534880
$607$	−12.9443	−0.525392	−0.262696	−	0.964879i	$-0.584612\pi$
$607$	−12.9443	−0.525392	−0.262696	+	0.964879i	$0.584612\pi$
$608$	43.4164	1.76077
$609$	−10.4721	−0.424352
$610$	0	0
$611$	8.94427	0.361847
$612$	−14.2918	−0.577712
$613$	−15.3050	−0.618161	−0.309081	−	0.951036i	$-0.600021\pi$
$613$	−15.3050	−0.618161	−0.309081	+	0.951036i	$0.600021\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−2.23607	−0.0900937
$617$	−6.58359	−0.265045	−0.132523	−	0.991180i	$-0.542308\pi$
$617$	−6.58359	−0.265045	−0.132523	+	0.991180i	$0.542308\pi$
$618$	21.3050	0.857011
$619$	11.1246	0.447136	0.223568	−	0.974688i	$-0.428230\pi$
$619$	11.1246	0.447136	0.223568	+	0.974688i	$0.428230\pi$
$620$	0	0
$621$	13.6656	0.548383
$622$	18.5410	0.743427
$623$	−2.00000	−0.0801283
$624$	4.00000	0.160128
$625$	0	0
$626$	33.4164	1.33559
$627$	−8.00000	−0.319489
$628$	−32.8328	−1.31017
$629$	27.4164	1.09316
$630$	0	0
$631$	−24.0000	−0.955425	−0.477712	−	0.878516i	$-0.658534\pi$
$631$	−24.0000	−0.955425	−0.477712	+	0.878516i	$0.658534\pi$
$632$	20.0000	0.795557
$633$	−17.1672	−0.682334
$634$	31.3050	1.24328
$635$	0	0
$636$	1.75078	0.0694228
$637$	−3.23607	−0.128218
$638$	18.9443	0.750011
$639$	15.4164	0.609864
$640$	0	0
$641$	−15.5279	−0.613314	−0.306657	−	0.951820i	$-0.599210\pi$
$641$	−15.5279	−0.613314	−0.306657	+	0.951820i	$0.599210\pi$
$642$	−11.0557	−0.436335
$643$	−11.1246	−0.438712	−0.219356	−	0.975645i	$-0.570396\pi$
$643$	−11.1246	−0.438712	−0.219356	+	0.975645i	$0.570396\pi$
$644$	7.41641	0.292247
$645$	0	0
$646$	−46.8328	−1.84261
$647$	−36.0689	−1.41801	−0.709007	−	0.705201i	$-0.750857\pi$
$647$	−36.0689	−1.41801	−0.709007	+	0.705201i	$0.750857\pi$
$648$	5.40325	0.212260
$649$	1.23607	0.0485199
$650$	0	0
$651$	3.41641	0.133900
$652$	10.2492	0.401391
$653$	−25.0557	−0.980506	−0.490253	−	0.871580i	$-0.663096\pi$
$653$	−25.0557	−0.980506	−0.490253	+	0.871580i	$0.663096\pi$
$654$	12.3607	0.483341
$655$	0	0
$656$	11.2361	0.438695
$657$	−1.12461	−0.0438753
$658$	−6.18034	−0.240935
$659$	−17.8885	−0.696839	−0.348419	−	0.937339i	$-0.613281\pi$
$659$	−17.8885	−0.696839	−0.348419	+	0.937339i	$0.613281\pi$
$660$	0	0
$661$	−40.8328	−1.58821	−0.794106	−	0.607779i	$-0.792061\pi$
$661$	−40.8328	−1.58821	−0.794106	+	0.607779i	$0.792061\pi$
$662$	31.0557	1.20702
$663$	−12.9443	−0.502714
$664$	−25.5279	−0.990673
$665$	0	0
$666$	27.8885	1.08066
$667$	−20.9443	−0.810965
$668$	−14.8328	−0.573899
$669$	12.5836	0.486510
$670$	0	0
$671$	7.23607	0.279345
$672$	−8.29180	−0.319863
$673$	21.4164	0.825542	0.412771	−	0.910835i	$-0.364561\pi$
$673$	21.4164	0.825542	0.412771	+	0.910835i	$0.364561\pi$
$674$	−25.7771	−0.992896
$675$	0	0
$676$	−7.58359	−0.291677
$677$	9.70820	0.373117	0.186558	−	0.982444i	$-0.440267\pi$
$677$	9.70820	0.373117	0.186558	+	0.982444i	$0.440267\pi$
$678$	5.52786	0.212296
$679$	17.4164	0.668380
$680$	0	0
$681$	−7.27864	−0.278918
$682$	−6.18034	−0.236657
$683$	5.88854	0.225319	0.112659	−	0.993634i	$-0.464063\pi$
$683$	5.88854	0.225319	0.112659	+	0.993634i	$0.464063\pi$
$684$	−28.5836	−1.09292
$685$	0	0
$686$	2.23607	0.0853735
$687$	−5.52786	−0.210901
$688$	8.00000	0.304997
$689$	−1.52786	−0.0582070
$690$	0	0
$691$	18.5410	0.705334	0.352667	−	0.935749i	$-0.385275\pi$
$691$	18.5410	0.705334	0.352667	+	0.935749i	$0.385275\pi$
$692$	38.2918	1.45564
$693$	−1.47214	−0.0559218
$694$	46.8328	1.77775
$695$	0	0
$696$	−23.4164	−0.887597
$697$	−36.3607	−1.37726
$698$	16.1803	0.612435
$699$	−11.6393	−0.440240
$700$	0	0
$701$	−15.5279	−0.586479	−0.293240	−	0.956039i	$-0.594733\pi$
$701$	−15.5279	−0.586479	−0.293240	+	0.956039i	$0.594733\pi$
$702$	−40.0000	−1.50970
$703$	54.8328	2.06806
$704$	13.0000	0.489956
$705$	0	0
$706$	44.4721	1.67373
$707$	4.76393	0.179166
$708$	−4.58359	−0.172262
$709$	−14.9443	−0.561244	−0.280622	−	0.959818i	$-0.590541\pi$
$709$	−14.9443	−0.561244	−0.280622	+	0.959818i	$0.590541\pi$
$710$	0	0
$711$	13.1672	0.493808
$712$	−4.47214	−0.167600
$713$	6.83282	0.255891
$714$	8.94427	0.334731
$715$	0	0
$716$	−26.8328	−1.00279
$717$	−12.2229	−0.456473
$718$	55.7771	2.08158
$719$	−51.4853	−1.92008	−0.960039	−	0.279867i	$-0.909710\pi$
$719$	−51.4853	−1.92008	−0.960039	+	0.279867i	$0.909710\pi$
$720$	0	0
$721$	7.70820	0.287069
$722$	−51.1803	−1.90474
$723$	−16.2229	−0.603337
$724$	−76.2492	−2.83378
$725$	0	0
$726$	−2.76393	−0.102579
$727$	−25.0132	−0.927687	−0.463843	−	0.885917i	$-0.653530\pi$
$727$	−25.0132	−0.927687	−0.463843	+	0.885917i	$0.653530\pi$
$728$	−7.23607	−0.268187
$729$	24.0557	0.890953
$730$	0	0
$731$	−25.8885	−0.957522
$732$	−26.8328	−0.991769
$733$	−8.76393	−0.323703	−0.161852	−	0.986815i	$-0.551747\pi$
$733$	−8.76393	−0.323703	−0.161852	+	0.986815i	$0.551747\pi$
$734$	−51.7082	−1.90858
$735$	0	0
$736$	−16.5836	−0.611279
$737$	14.4721	0.533088
$738$	−36.9868	−1.36150
$739$	24.9443	0.917590	0.458795	−	0.888542i	$-0.348281\pi$
$739$	24.9443	0.917590	0.458795	+	0.888542i	$0.348281\pi$
$740$	0	0
$741$	−25.8885	−0.951039
$742$	1.05573	0.0387570
$743$	−1.88854	−0.0692840	−0.0346420	−	0.999400i	$-0.511029\pi$
$743$	−1.88854	−0.0692840	−0.0346420	+	0.999400i	$0.511029\pi$
$744$	7.63932	0.280071
$745$	0	0
$746$	13.4164	0.491210
$747$	−16.8065	−0.614918
$748$	−9.70820	−0.354967
$749$	−4.00000	−0.146157
$750$	0	0
$751$	29.5279	1.07749	0.538744	−	0.842470i	$-0.318899\pi$
$751$	29.5279	1.07749	0.538744	+	0.842470i	$0.318899\pi$
$752$	2.76393	0.100790
$753$	5.30495	0.193323
$754$	61.3050	2.23259
$755$	0	0
$756$	16.5836	0.603139
$757$	−15.8885	−0.577479	−0.288739	−	0.957408i	$-0.593236\pi$
$757$	−15.8885	−0.577479	−0.288739	+	0.957408i	$0.593236\pi$
$758$	−83.4164	−3.02982
$759$	3.05573	0.110916
$760$	0	0
$761$	−31.5967	−1.14538	−0.572691	−	0.819772i	$-0.694100\pi$
$761$	−31.5967	−1.14538	−0.572691	+	0.819772i	$0.694100\pi$
$762$	8.44582	0.305960
$763$	4.47214	0.161902
$764$	−9.16718	−0.331657
$765$	0	0
$766$	−10.4033	−0.375885
$767$	4.00000	0.144432
$768$	−11.1246	−0.401425
$769$	18.2918	0.659619	0.329810	−	0.944047i	$-0.393015\pi$
$769$	18.2918	0.659619	0.329810	+	0.944047i	$0.393015\pi$
$770$	0	0
$771$	7.41641	0.267095
$772$	−35.6656	−1.28363
$773$	38.3607	1.37974	0.689869	−	0.723934i	$-0.257668\pi$
$773$	38.3607	1.37974	0.689869	+	0.723934i	$0.257668\pi$
$774$	−26.3344	−0.946569
$775$	0	0
$776$	38.9443	1.39802
$777$	−10.4721	−0.375686
$778$	−35.5279	−1.27374
$779$	−72.7214	−2.60551
$780$	0	0
$781$	10.4721	0.374722
$782$	17.8885	0.639693
$783$	−46.8328	−1.67367
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	−60.4984	−2.15791
$787$	43.4164	1.54763	0.773814	−	0.633413i	$-0.218347\pi$
$787$	43.4164	1.54763	0.773814	+	0.633413i	$0.218347\pi$
$788$	6.00000	0.213741
$789$	0	0
$790$	0	0
$791$	2.00000	0.0711118
$792$	−3.29180	−0.116969
$793$	23.4164	0.831541
$794$	−80.2492	−2.84794
$795$	0	0
$796$	−6.54102	−0.231840
$797$	14.9443	0.529353	0.264677	−	0.964337i	$-0.414735\pi$
$797$	14.9443	0.529353	0.264677	+	0.964337i	$0.414735\pi$
$798$	17.8885	0.633248
$799$	−8.94427	−0.316426
$800$	0	0
$801$	−2.94427	−0.104031
$802$	−51.3050	−1.81164
$803$	−0.763932	−0.0269586
$804$	−53.6656	−1.89264
$805$	0	0
$806$	−20.0000	−0.704470
$807$	16.5836	0.583770
$808$	10.6525	0.374753
$809$	21.0557	0.740280	0.370140	−	0.928976i	$-0.379310\pi$
$809$	21.0557	0.740280	0.370140	+	0.928976i	$0.379310\pi$
$810$	0	0
$811$	−34.8328	−1.22315	−0.611573	−	0.791188i	$-0.709463\pi$
$811$	−34.8328	−1.22315	−0.611573	+	0.791188i	$0.709463\pi$
$812$	−25.4164	−0.891941
$813$	−12.9443	−0.453975
$814$	18.9443	0.663996
$815$	0	0
$816$	−4.00000	−0.140028
$817$	−51.7771	−1.81145
$818$	−20.4033	−0.713383
$819$	−4.76393	−0.166465
$820$	0	0
$821$	44.8328	1.56468	0.782338	−	0.622854i	$-0.214027\pi$
$821$	44.8328	1.56468	0.782338	+	0.622854i	$0.214027\pi$
$822$	45.5279	1.58797
$823$	14.1115	0.491894	0.245947	−	0.969283i	$-0.420901\pi$
$823$	14.1115	0.491894	0.245947	+	0.969283i	$0.420901\pi$
$824$	17.2361	0.600447
$825$	0	0
$826$	−2.76393	−0.0961695
$827$	12.9443	0.450116	0.225058	−	0.974345i	$-0.427743\pi$
$827$	12.9443	0.450116	0.225058	+	0.974345i	$0.427743\pi$
$828$	10.9180	0.379425
$829$	36.8328	1.27926	0.639628	−	0.768684i	$-0.279088\pi$
$829$	36.8328	1.27926	0.639628	+	0.768684i	$0.279088\pi$
$830$	0	0
$831$	24.5836	0.852795
$832$	42.0689	1.45848
$833$	3.23607	0.112123
$834$	4.22291	0.146227
$835$	0	0
$836$	−19.4164	−0.671531
$837$	15.2786	0.528107
$838$	−55.1246	−1.90425
$839$	44.0689	1.52143	0.760713	−	0.649088i	$-0.224849\pi$
$839$	44.0689	1.52143	0.760713	+	0.649088i	$0.224849\pi$
$840$	0	0
$841$	42.7771	1.47507
$842$	−50.0000	−1.72311
$843$	−4.36068	−0.150190
$844$	−41.6656	−1.43419
$845$	0	0
$846$	−9.09830	−0.312806
$847$	−1.00000	−0.0343604
$848$	−0.472136	−0.0162132
$849$	−36.9443	−1.26792
$850$	0	0
$851$	−20.9443	−0.717960
$852$	−38.8328	−1.33039
$853$	30.6525	1.04952	0.524760	−	0.851250i	$-0.324155\pi$
$853$	30.6525	1.04952	0.524760	+	0.851250i	$0.324155\pi$
$854$	−16.1803	−0.553680
$855$	0	0
$856$	−8.94427	−0.305709
$857$	−15.2361	−0.520454	−0.260227	−	0.965547i	$-0.583797\pi$
$857$	−15.2361	−0.520454	−0.260227	+	0.965547i	$0.583797\pi$
$858$	−8.94427	−0.305352
$859$	−26.5410	−0.905568	−0.452784	−	0.891620i	$-0.649569\pi$
$859$	−26.5410	−0.905568	−0.452784	+	0.891620i	$0.649569\pi$
$860$	0	0
$861$	13.8885	0.473320
$862$	−26.8328	−0.913929
$863$	3.05573	0.104018	0.0520091	−	0.998647i	$-0.483438\pi$
$863$	3.05573	0.104018	0.0520091	+	0.998647i	$0.483438\pi$
$864$	−37.0820	−1.26156
$865$	0	0
$866$	−18.9443	−0.643753
$867$	−8.06888	−0.274034
$868$	8.29180	0.281442
$869$	8.94427	0.303414
$870$	0	0
$871$	46.8328	1.58687
$872$	10.0000	0.338643
$873$	25.6393	0.867760
$874$	35.7771	1.21018
$875$	0	0
$876$	2.83282	0.0957120
$877$	−14.5836	−0.492453	−0.246226	−	0.969212i	$-0.579191\pi$
$877$	−14.5836	−0.492453	−0.246226	+	0.969212i	$0.579191\pi$
$878$	−23.4164	−0.790265
$879$	31.0557	1.04748
$880$	0	0
$881$	2.58359	0.0870434	0.0435217	−	0.999052i	$-0.486142\pi$
$881$	2.58359	0.0870434	0.0435217	+	0.999052i	$0.486142\pi$
$882$	3.29180	0.110841
$883$	8.94427	0.300999	0.150499	−	0.988610i	$-0.451912\pi$
$883$	8.94427	0.300999	0.150499	+	0.988610i	$0.451912\pi$
$884$	−31.4164	−1.05665
$885$	0	0
$886$	−55.7771	−1.87387
$887$	4.36068	0.146417	0.0732086	−	0.997317i	$-0.476676\pi$
$887$	4.36068	0.146417	0.0732086	+	0.997317i	$0.476676\pi$
$888$	−23.4164	−0.785803
$889$	3.05573	0.102486
$890$	0	0
$891$	2.41641	0.0809527
$892$	30.5410	1.02259
$893$	−17.8885	−0.598617
$894$	−38.6950	−1.29416
$895$	0	0
$896$	−15.6525	−0.522913
$897$	9.88854	0.330169
$898$	63.6656	2.12455
$899$	−23.4164	−0.780981
$900$	0	0
$901$	1.52786	0.0509005
$902$	−25.1246	−0.836558
$903$	9.88854	0.329070
$904$	4.47214	0.148741
$905$	0	0
$906$	−24.7214	−0.821312
$907$	−22.4721	−0.746175	−0.373088	−	0.927796i	$-0.621701\pi$
$907$	−22.4721	−0.746175	−0.373088	+	0.927796i	$0.621701\pi$
$908$	−17.6656	−0.586255
$909$	7.01316	0.232612
$910$	0	0
$911$	42.4721	1.40716	0.703582	−	0.710614i	$-0.251583\pi$
$911$	42.4721	1.40716	0.703582	+	0.710614i	$0.251583\pi$
$912$	−8.00000	−0.264906
$913$	−11.4164	−0.377828
$914$	−64.4721	−2.13255
$915$	0	0
$916$	−13.4164	−0.443291
$917$	−21.8885	−0.722823
$918$	40.0000	1.32020
$919$	41.8885	1.38178	0.690888	−	0.722962i	$-0.257220\pi$
$919$	41.8885	1.38178	0.690888	+	0.722962i	$0.257220\pi$
$920$	0	0
$921$	11.0557	0.364299
$922$	27.2361	0.896972
$923$	33.8885	1.11546
$924$	3.70820	0.121991
$925$	0	0
$926$	−12.3607	−0.406197
$927$	11.3475	0.372702
$928$	56.8328	1.86563
$929$	−52.2492	−1.71424	−0.857121	−	0.515116i	$-0.827749\pi$
$929$	−52.2492	−1.71424	−0.857121	+	0.515116i	$0.827749\pi$
$930$	0	0
$931$	6.47214	0.212116
$932$	−28.2492	−0.925334
$933$	−10.2492	−0.335545
$934$	53.8197	1.76103
$935$	0	0
$936$	−10.6525	−0.348187
$937$	10.6525	0.348001	0.174001	−	0.984746i	$-0.444331\pi$
$937$	10.6525	0.348001	0.174001	+	0.984746i	$0.444331\pi$
$938$	−32.3607	−1.05661
$939$	−18.4721	−0.602815
$940$	0	0
$941$	7.59675	0.247647	0.123823	−	0.992304i	$-0.460484\pi$
$941$	7.59675	0.247647	0.123823	+	0.992304i	$0.460484\pi$
$942$	30.2492	0.985573
$943$	27.7771	0.904546
$944$	1.23607	0.0402306
$945$	0	0
$946$	−17.8885	−0.581607
$947$	5.16718	0.167911	0.0839555	−	0.996470i	$-0.473245\pi$
$947$	5.16718	0.167911	0.0839555	+	0.996470i	$0.473245\pi$
$948$	−33.1672	−1.07722
$949$	−2.47214	−0.0802489
$950$	0	0
$951$	−17.3050	−0.561152
$952$	7.23607	0.234522
$953$	−22.9443	−0.743238	−0.371619	−	0.928385i	$-0.621197\pi$
$953$	−22.9443	−0.743238	−0.371619	+	0.928385i	$0.621197\pi$
$954$	1.55418	0.0503183
$955$	0	0
$956$	−29.6656	−0.959455
$957$	−10.4721	−0.338516
$958$	−30.2492	−0.977308
$959$	16.4721	0.531913
$960$	0	0
$961$	−23.3607	−0.753570
$962$	61.3050	1.97655
$963$	−5.88854	−0.189756
$964$	−39.3738	−1.26815
$965$	0	0
$966$	−6.83282	−0.219842
$967$	13.8885	0.446625	0.223313	−	0.974747i	$-0.428313\pi$
$967$	13.8885	0.446625	0.223313	+	0.974747i	$0.428313\pi$
$968$	−2.23607	−0.0718699
$969$	25.8885	0.831660
$970$	0	0
$971$	11.1246	0.357006	0.178503	−	0.983939i	$-0.442875\pi$
$971$	11.1246	0.357006	0.178503	+	0.983939i	$0.442875\pi$
$972$	40.7902	1.30835
$973$	1.52786	0.0489811
$974$	−81.3050	−2.60518
$975$	0	0
$976$	7.23607	0.231621
$977$	−22.9443	−0.734052	−0.367026	−	0.930211i	$-0.619624\pi$
$977$	−22.9443	−0.734052	−0.367026	+	0.930211i	$0.619624\pi$
$978$	−9.44272	−0.301945
$979$	−2.00000	−0.0639203
$980$	0	0
$981$	6.58359	0.210198
$982$	0	0
$983$	−21.8197	−0.695939	−0.347970	−	0.937506i	$-0.613129\pi$
$983$	−21.8197	−0.695939	−0.347970	+	0.937506i	$0.613129\pi$
$984$	31.0557	0.990020
$985$	0	0
$986$	−61.3050	−1.95235
$987$	3.41641	0.108745
$988$	−62.8328	−1.99898
$989$	19.7771	0.628875
$990$	0	0
$991$	54.2492	1.72328	0.861642	−	0.507517i	$-0.169437\pi$
$991$	54.2492	1.72328	0.861642	+	0.507517i	$0.169437\pi$
$992$	−18.5410	−0.588678
$993$	−17.1672	−0.544784
$994$	−23.4164	−0.742723
$995$	0	0
$996$	42.3344	1.34142
$997$	−1.34752	−0.0426765	−0.0213383	−	0.999772i	$-0.506793\pi$
$997$	−1.34752	−0.0426765	−0.0213383	+	0.999772i	$0.506793\pi$
$998$	−3.41641	−0.108145
$999$	−46.8328	−1.48172

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1925.2.a.r.1.1		2
5.2	odd	4		1925.2.b.h.1849.2		4
5.3	odd	4		1925.2.b.h.1849.3		4
5.4	even	2		77.2.a.d.1.2	✓	2
15.14	odd	2		693.2.a.h.1.1		2
20.19	odd	2		1232.2.a.m.1.2		2
35.4	even	6		539.2.e.i.177.1		4
35.9	even	6		539.2.e.i.67.1		4
35.19	odd	6		539.2.e.j.67.1		4
35.24	odd	6		539.2.e.j.177.1		4
35.34	odd	2		539.2.a.f.1.2		2
40.19	odd	2		4928.2.a.bv.1.1		2
40.29	even	2		4928.2.a.bm.1.2		2
55.4	even	10		847.2.f.n.148.1		4
55.9	even	10		847.2.f.a.323.1		4
55.14	even	10		847.2.f.n.372.1		4
55.19	odd	10		847.2.f.b.372.1		4
55.24	odd	10		847.2.f.m.323.1		4
55.29	odd	10		847.2.f.b.148.1		4
55.39	odd	10		847.2.f.m.729.1		4
55.49	even	10		847.2.f.a.729.1		4
55.54	odd	2		847.2.a.f.1.1		2
105.104	even	2		4851.2.a.y.1.1		2
140.139	even	2		8624.2.a.ce.1.1		2
165.164	even	2		7623.2.a.bl.1.2		2
385.384	even	2		5929.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.a.d.1.2	✓	2	5.4	even	2
539.2.a.f.1.2		2	35.34	odd	2
539.2.e.i.67.1		4	35.9	even	6
539.2.e.i.177.1		4	35.4	even	6
539.2.e.j.67.1		4	35.19	odd	6
539.2.e.j.177.1		4	35.24	odd	6
693.2.a.h.1.1		2	15.14	odd	2
847.2.a.f.1.1		2	55.54	odd	2
847.2.f.a.323.1		4	55.9	even	10
847.2.f.a.729.1		4	55.49	even	10
847.2.f.b.148.1		4	55.29	odd	10
847.2.f.b.372.1		4	55.19	odd	10
847.2.f.m.323.1		4	55.24	odd	10
847.2.f.m.729.1		4	55.39	odd	10
847.2.f.n.148.1		4	55.4	even	10
847.2.f.n.372.1		4	55.14	even	10
1232.2.a.m.1.2		2	20.19	odd	2
1925.2.a.r.1.1		2	1.1	even	1	trivial
1925.2.b.h.1849.2		4	5.2	odd	4
1925.2.b.h.1849.3		4	5.3	odd	4
4851.2.a.y.1.1		2	105.104	even	2
4928.2.a.bm.1.2		2	40.29	even	2
4928.2.a.bv.1.1		2	40.19	odd	2
5929.2.a.m.1.1		2	385.384	even	2
7623.2.a.bl.1.2		2	165.164	even	2
8624.2.a.ce.1.1		2	140.139	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1925 = 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1925.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -2.76393 q^{6} -1.00000 q^{7} -2.23607 q^{8} -1.47214 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} +1.23607 q^{3} +3.00000 q^{4} -2.76393 q^{6} -1.00000 q^{7} -2.23607 q^{8} -1.47214 q^{9} -1.00000 q^{11} +3.70820 q^{12} -3.23607 q^{13} +2.23607 q^{14} -1.00000 q^{16} +3.23607 q^{17} +3.29180 q^{18} +6.47214 q^{19} -1.23607 q^{21} +2.23607 q^{22} -2.47214 q^{23} -2.76393 q^{24} +7.23607 q^{26} -5.52786 q^{27} -3.00000 q^{28} +8.47214 q^{29} -2.76393 q^{31} +6.70820 q^{32} -1.23607 q^{33} -7.23607 q^{34} -4.41641 q^{36} +8.47214 q^{37} -14.4721 q^{38} -4.00000 q^{39} -11.2361 q^{41} +2.76393 q^{42} -8.00000 q^{43} -3.00000 q^{44} +5.52786 q^{46} -2.76393 q^{47} -1.23607 q^{48} +1.00000 q^{49} +4.00000 q^{51} -9.70820 q^{52} +0.472136 q^{53} +12.3607 q^{54} +2.23607 q^{56} +8.00000 q^{57} -18.9443 q^{58} -1.23607 q^{59} -7.23607 q^{61} +6.18034 q^{62} +1.47214 q^{63} -13.0000 q^{64} +2.76393 q^{66} -14.4721 q^{67} +9.70820 q^{68} -3.05573 q^{69} -10.4721 q^{71} +3.29180 q^{72} +0.763932 q^{73} -18.9443 q^{74} +19.4164 q^{76} +1.00000 q^{77} +8.94427 q^{78} -8.94427 q^{79} -2.41641 q^{81} +25.1246 q^{82} +11.4164 q^{83} -3.70820 q^{84} +17.8885 q^{86} +10.4721 q^{87} +2.23607 q^{88} +2.00000 q^{89} +3.23607 q^{91} -7.41641 q^{92} -3.41641 q^{93} +6.18034 q^{94} +8.29180 q^{96} -17.4164 q^{97} -2.23607 q^{98} +1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 6 q^{4} - 10 q^{6} - 2 q^{7} + 6 q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + 6 * q^4 - 10 * q^6 - 2 * q^7 + 6 * q^9	\( 2 q - 2 q^{3} + 6 q^{4} - 10 q^{6} - 2 q^{7} + 6 q^{9} - 2 q^{11} - 6 q^{12} - 2 q^{13} - 2 q^{16} + 2 q^{17} + 20 q^{18} + 4 q^{19} + 2 q^{21} + 4 q^{23} - 10 q^{24} + 10 q^{26} - 20 q^{27} - 6 q^{28} + 8 q^{29} - 10 q^{31} + 2 q^{33} - 10 q^{34} + 18 q^{36} + 8 q^{37} - 20 q^{38} - 8 q^{39} - 18 q^{41} + 10 q^{42} - 16 q^{43} - 6 q^{44} + 20 q^{46} - 10 q^{47} + 2 q^{48} + 2 q^{49} + 8 q^{51} - 6 q^{52} - 8 q^{53} - 20 q^{54} + 16 q^{57} - 20 q^{58} + 2 q^{59} - 10 q^{61} - 10 q^{62} - 6 q^{63} - 26 q^{64} + 10 q^{66} - 20 q^{67} + 6 q^{68} - 24 q^{69} - 12 q^{71} + 20 q^{72} + 6 q^{73} - 20 q^{74} + 12 q^{76} + 2 q^{77} + 22 q^{81} + 10 q^{82} - 4 q^{83} + 6 q^{84} + 12 q^{87} + 4 q^{89} + 2 q^{91} + 12 q^{92} + 20 q^{93} - 10 q^{94} + 30 q^{96} - 8 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 6 * q^4 - 10 * q^6 - 2 * q^7 + 6 * q^9 - 2 * q^11 - 6 * q^12 - 2 * q^13 - 2 * q^16 + 2 * q^17 + 20 * q^18 + 4 * q^19 + 2 * q^21 + 4 * q^23 - 10 * q^24 + 10 * q^26 - 20 * q^27 - 6 * q^28 + 8 * q^29 - 10 * q^31 + 2 * q^33 - 10 * q^34 + 18 * q^36 + 8 * q^37 - 20 * q^38 - 8 * q^39 - 18 * q^41 + 10 * q^42 - 16 * q^43 - 6 * q^44 + 20 * q^46 - 10 * q^47 + 2 * q^48 + 2 * q^49 + 8 * q^51 - 6 * q^52 - 8 * q^53 - 20 * q^54 + 16 * q^57 - 20 * q^58 + 2 * q^59 - 10 * q^61 - 10 * q^62 - 6 * q^63 - 26 * q^64 + 10 * q^66 - 20 * q^67 + 6 * q^68 - 24 * q^69 - 12 * q^71 + 20 * q^72 + 6 * q^73 - 20 * q^74 + 12 * q^76 + 2 * q^77 + 22 * q^81 + 10 * q^82 - 4 * q^83 + 6 * q^84 + 12 * q^87 + 4 * q^89 + 2 * q^91 + 12 * q^92 + 20 * q^93 - 10 * q^94 + 30 * q^96 - 8 * q^97 - 6 * q^99

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